gravity chains: estimating bilateral trade flows when parts ......for example, rauch (1999), brun et...

NBER WORKING PAPER SERIES

GRAVITY CHAINS: ESTIMATING BILATERAL TRADE FLOWS WHEN PARTSAND COMPONENTS TRADE IS IMPORTANT

Richard BaldwinDaria Taglioni

Working Paper 16672http://www.nber.org/papers/w16672

NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

Cambridge, MA 02138January 2011

We would like to thank participants at workshop at the WTO and Oxford. The views expressed inthis paper are those of the authors and do not necessarily represent those of the European Central Bankor the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.

© 2011 by Richard Baldwin and Daria Taglioni. All rights reserved. Short sections of text, not to exceedtwo paragraphs, may be quoted without explicit permission provided that full credit, including © notice,is given to the source.

Gravity Chains: Estimating Bilateral Trade Flows When Parts And Components Trade Is ImportantRichard Baldwin and Daria TaglioniNBER Working Paper No. 16672January 2011, Revised June 2011JEL No. F1,F15

ABSTRACT

Trade is measured on a gross sales basis while GDP is measured on a net sales basis, i.e. value added.The rapid internationalisation of production in the last two decades has meant that gross trade flowsare increasingly unrepresentative of the value added flows. This fact has important implications forthe estimation of the gravity equation. We present empirical evidence that the standard gravity equationperforms poorly by some measures when it is applied to bilateral flows where parts and components trade isimportant. We also provide a simple theoretical foundation for a modified gravity equation that issuited to explaining trade where international supply chains are important.

Richard BaldwinGraduate Institute, GenevaCigale 21010 LausanneSWITZERLANDand CEPRand also [email protected]

Daria TaglioniCentre for Trade and Economic IntegrationInstitut de hautes études internationales et du développementThe Graduate Institute of International and Development Studies Case postale 136 - CH - 1211 Genève 21 - [email protected]

2

1. INTRODUCTION

Trade is measured on a gross sales basis while GDP is measured on a value added basis. For the

first decades of the postwar period, this distinction was relatively unimportant. Trade in

intermediates was always important, but it was quite proportional to trade in final goods. The

rapid internationalisation of supply chains in the last two decades has changed this (Yi 2003).

Indeed, such trade has in recent decades boomed between advanced nations and emerging

economies as well as among emerging nations – especially in Asia, where the phenomenon is

known as “Factory Asia”. There are, however, similar supply chains in Europe and between the

US and Mexico (Kimura, Fukunari, Yuya Takahashi and Kazunobu Hayakawa 2007). As a

result, gross trade flows are increasingly unrepresentative of the value-added flows. This fact has

important policy implications (Lamy 2010), but it also has important implications for one of

trade economists‟ standard tools – the gravity equation.

The basic point is simple. The standard gravity equation is derived from a consumer expenditure

equation with the relative price eliminated using a general equilibrium constraint (Anderson

1979, Bergstrand 1985, 1989, 1990). The corresponding econometrics widely used today is

based on this theory (Anderson and Van Wincoop 2003). As such the standard formulation –

bilateral trade regressed on the two GDPs, bilateral distance and other controls – is best adapted

to explaining trade in consumer goods. When consumer trade dominates, the GDP of the

destination nation is a good proxy for the demand shifter in the consumer expenditure equation;

the GDP of the origin nation is a good proxy of its total supply. By contrast, when international

trade in intermediate goods dominates, the use of GDPs for the supply and demand proxies is

less appropriate.

Consider, for instance, the determinants of Thai imports of auto parts from the Philippines. The

standard formulation would use Thai GDP to explain Thailand‟s import demand, however, the

underlying demand for parts is generated by Thai gross production of autos, not its value-added

in autos. As long as the ratio of local to imported content does not change, value added is a

reasonable proxy for gross output, so the standard regression is likely to give reasonable results.

However, for regions where production networks are emerging, value added can be expected to

be a poor proxy.

Why do incorrectly specified mass variables matter? A large number of gravity studies focus on

variables that vary across country pairs – say free trade agreements, cultural ties, or immigrant

networks. The most recent of these studies employ estimators that control for the mass variables

with fixed effects. Such studies do not suffer from mass-variable mis-specification and so are

unaffected by our critique. There are however a number of recent studies – especially concerning

the „distance puzzle‟ that do proxy for the production and demand variables with GDP. It is these

studies that our work speaks to.

For example, Rauch (1999), Brun et al (2005), Berthelon and Freund (2008), and Jacks et al

(2008) use GDP as the mass variable when they decompose the change in the trade flow into the

effects of income changes and trade cost changes; Anderson and Van Wincoop (2003) also use

GDP as the mass variable in one of their estimation techniques. Since most of these studies are

concerned with a broad set of nations and commodities, the mis-specification of the mass

variable probably has a minor impact on the results – as the findings of Bergstrand and Egger

(2010) showed. More worrying, however, is the use by authors that focus on trade in parts and

3

components such as Athukorala and Yamashita (2006), Kimura et al (2007), Yokota and

Kazuhiko (2008), and Ando and Kimura (2009). These papers all use the consumer good version

of the gravity model to describe parts and components trade and thus have mis-specified the

mass variable.

Literature review

There is nothing new about trade in intermediates. Intermediates have long been important in the

trade between the US and Canada; the 1965 US-Canada Auto Pact, for example, explicitly

targeted preferential tariff reductions on cars and cars parts. It has also long been important

within Western Europe as early studies of the EEC demonstrated (e.g. Dreze 1961, Verdoorn

1960, and Balassa 1965, 1966). The famous book by Grubel and Lloyd (1975), made clear that

much of intra-industry trade was in intermediates, not final goods, and the importance of

intermediates was reflected in early work by well-known theorists. For example, Vaneck (1963)

presents an extension of the Heckscher-Ohlin model that allows for intermediates trade, and

Ethier (1981) casts his model of intra-industry trade in a world where all trade was in

intermediates.

As better data and computing technology became available, the importance of intermediates in

trade was rediscovered and documented more thoroughly. In the context of efforts to understand

the impact of the EU‟s Single Market Programme, European scholars focused on the role of

intermediates. For example, Greenaway and Milner (1987) list this as one of the „unresolved

issues‟, writing “it is becoming increasingly obvious that a significant proportion of measured

IIT is accounted for by trade in parts and components. [Nevertheless,] most of the models

developed so far assume trade in final goods. The modelling of trade in intermediates needs to be

explored further." The issue attracted renewed interest following development of the new trade

theory in the 1980s (Helpman and Krugman 1985)1 and again in the 1990s with Jones and

Kierzkowski (1990), and Hummels, Rapoport and Yi (1998)2, and more recently Kimura,

Takahashi and Hayakawa (2007), and Grossman and Rossi-Hansberg (2008).

The traditional gravity model was developed in the 1960s to explain factory-to-consumer trade

(Tinbergen 1962, Poyhonen 1963, Linnemann 1966). This concept is at the heart of the first clear

microfoundations of the gravity equation – the seminal Anderson (1979).3 This article proposed a

theoretical explanation of the gravity equation based on CES preferences when nations make a

single differentiated product. Anderson and Van Wincoop (2003) use the Anderson (1979)

theory to develop appropriate econometric techniques. Subsequent theoretical refinements have

focused on showing that the gravity equation can be derived from many different theoretical

1 As illustrated by the Brookings Institution book “The global factory: Foreign assembly in

international trade” (Grunwald and Flam 1985).

2 Feenstra (1998) for a survey of the 1990s literature.

3 Leamer and Stern (1970) informally discusses three economic mechanism that might generate

the gravity equations but these were based on rather exotic economic logics; Anderson (1979)

was the first to provide clear microfoundations that rely only on assumptions that would strike

present-day readers as absolutely standard.

4

frameworks (including monopolistic competition, and Melitz-type trade models with

heterogeneous firms).4

Studies on the gravity equations applicability to intermediate goods trade are more limited. These

include Egger and Egger (2004), and Baldone et al (2007). The study that is closest to ours is

Bergstrand and Egger (2010). These authors develop a computable general equilibrium model

that explains the bilateral flows of final goods, intermediate goods and FDI. Calibration and

simulation of the model suggests a theoretical rationale for estimating a near-standard gravity

model for the three types of bilateral flows. Using a large dataset on bilateral flows of final and

intermediate goods trade, and a dataset on bilateral FDI flows, they estimate the three equations

and find that the standard gravity variables all have the expected size and magnitude.

The value added of our paper is primarily empirical – to show that the standard gravity

specification performs poorly when applied to flows where trade in intermediates is important.

Moreover, the failures line up with the predictions of our simple theory model that suggests a

gravity equation formulation that is appropriate to intermediates trade. Note that when we

perform the estimates on data pooled across a wide range of nations – as do Bergstrand and

Egger (2010) – we find the same results, namely that the standard specification performs well.

We believe the difference in the results is due to the fact that for many trade flows, the pattern of

trade in intermediates is quite proportional to trade in final goods. This is especially for trade

among developed nations.

Plan of the paper

The paper starts with simple theory that generates a number of testable hypotheses. We then

confront these hypotheses with the data and find that the estimated coefficients deviate from

standard results in the way that the simple theory says they should. The key results are that the

standard economic mass variable, which reflects consumer demand, does not perform well when

it comes to bilateral trade flows where intermediates are dominant. Finally, we consider new

proxies for the economic mass variables and show that using the wrong mass variable may bias

estimates of other coefficients.

2. THEORY

To introduce notation and fix ideas, we review the standard gravity derivation following Baldwin

and Taglioni (2007).5 Using the well-known CES preference structure for differentiated varieties,

spending in nation-d („d‟ for destination) on a variety produced in nation-o („o‟ for origin) is:

4 On the monopolistic competition frameworks see Krugman (1980), Bergstrand (1985, 1989),

Helpman and Krugman, (1985); on the Heckscher-Ohlin model see Deardorff (1998), on

Ricardian models see Eaton and Kortum (2001); on Melitz (2003) model applications, see

Chaney (2008), and Helpman, Melitz and Rubinstein (2008).

5 Another well-known derivation is from Helpman and Krugman (1985); they start from (1) and

make supply-side assumptions that turns po into a constant, but makes nod proportional to nation-

o‟s GDP so the resulting gravity equation is similar – at least in the case of frictionless trade (the

case they worked with in 1985).

5

1;

1

d

d

od

od EP

pv (1)

where odv is the expenditure in destination country-d, pod is the consumer price inside nation-d

of a variety made in nation-o, dP is the nation-d CES price index of all varieties, is the

elasticity of substitution among varieties ( > 1 is assumed throughout), and dE is the nation-d

consumer expenditure.

From the well-known profit maximization exercise of producers based in nation-o,

odoodod mp , where od is the optimal price mark-up, om is the marginal costs, and od is

the bilateral trade cost factor, i.e. 1 plus the ad valorem tariff equivalent of all natural and

manmade barriers. The mark-up is identical for all destinations if we assume perfect competition

or Dixit-Stiglitz monopolistic competition; in these cases, the price variation is characterised by

“mill pricing”, i.e. 100% pass through of trade costs to consumers in the destination market.6

Here we work with Dixit-Stiglitz competition exclusively, so the mark-up is always /(-1).

This means the local consumer price is ooooo mp ))1/(( , where oo is unity as we assume

away internal trade barriers. Using this and summing over all varieties (assuming symmetry of

varieties by origin nation for convenience), we have:

dd

od

ooood EP

pnV

1

11

(2)

where odV is the aggregate value of the bilateral flow (measured in terms of the numeraire) from

nation-o to nation-d; on is the number (mass) of nation-o varieties (all of which are sold in

nation-d as per the well-known results of the Dixit-Stiglitz-Krugman model).

To turn this expenditure function (with optimal prices) into a gravity equation, we impose the

market-clearing condition. Supply and demand match when (2) – summed across all destinations

(including nation-o‟s sales to itself) – equals nation-o‟s output. When there is no international

sourcing of parts, the nation‟s output is its GDP, denoted here as Yo. Thus the market-clearing

condition is: d ddodoooo EPpnY111 . Solving this we obtain that ooooo Ypn

/1 where o

is the usual market-potential index (namely, the sum of partners‟ market sizes weighted by a

distance-related weight that places lower weight on more remote destinations); specifically it is

d ddodo EP11 . Plugging this into (2) yields the traditional gravity equation:

od

odododP

YEV

111

1

(3)

Here Pd is the nation-d CES price index, while o is the nation-o market-potential index. It has

become common to label the product odP 1

as the “multilateral trade resistance” term.

6 If one works with the Ottaviano Tabuchi and Thisse (2002) monopolistic competition

framework, the mark-up varies bilaterally and so mill-pricing is not optimal.

6

However, it is insightful to keep in mind the fact that “multilateral trade resistance” is a

combination of two well-known, well-understood, and frequently measured components.

In the typical gravity estimation, Ed is proxied with nation-d‟s GDP, Yd is proxied with nation-

o‟s GDP, and is proxied with bilateral distance.

2.1. Gravity when parts and components trade is important

To extend the gravity equation to allow for parts and components trade among firms, we need a

trade model where intermediate goods trade is explicitly addressed. It proves convenient to work

with the Krugman and Venables (1996) “vertical linkages” model which focuses squarely on the

role of intermediate goods. Here we present the basic assumptions and the manipulations that

produce the modified gravity equation.

Krugman and Venables (1996) works with the standard new economic geography model where

each nation has two sectors (a Walrasian sector, A, and a Dixit-Stiglitz monopolistic competition

sector M), and a single primary factor, labour L. Production of A requires only L, but production

of each variety of X requires L and a CES composite of all varieties as intermediate inputs (i.e.

each variety is purchased both for final consumption and for use as an intermediate). Following

Krugman and Venables (1996), the CES aggregate on the supply side is isomorphic to the

standard CES consumption aggregate.

The indirect utility function for the typical consumer is:

)1/(111 ;;/

Gi iAcc dipPPpPPIV (4)

where I is consumer income, Pc is the ideal consumer price index, pA is the price of A, the

parameter “” is the Cobb-Douglas expenditure share for M-sector goods, is the elasticity of

substitution among varieties, P is the CES price index for M varieties, pi is the consumer price of

variety i, and G is the set of varieties available.

The cost function of a typical firm in a typical country is:

PwxaFxPwC X 1],,[ (5)

Here x is the output of a typical variety, F and aX are cost parameters, w is the wage, and is the

Cobb-Douglas cost share for intermediate inputs.7

As noted above, mill pricing is optimal under Dixit-Stiglitz monopolistic competition. This,

combined with the identity of the elasticity of substitution, , for each good‟s use in

consumption and production, tells us that the price of each variety will be identical across the

two types of customers. Choosing units such that aX = 1-1/, the landed price will be:

doPwp ooodod ,;1

(6)

7 The assumption that the Cobb-Douglas parameter is identical in the consumer and producer

CES price index is one of the strategic implications in the Krugman-Venables model; see their

book for a careful examination of what happens when this is relaxed (Fujitu, Krugman and

Venables 1999). The standard conclusion is that it does not qualitatively change results but it

does significantly complicate the analysis in a way that requires numerical simulation.

7

Using Shepard‟s and Hotelling‟s lemmas on (4) and (5), and adding the total demand for

purchasers located in nation-d, we have an expression that is isomorphic to (2) except the

definition of E now includes purchases by customers using the goods as intermediates:

)(;1

1

1

ddddd

d

od

ooood CnIEEP

pnV

(7)

where Id is nation-d‟s consumer income and Cd is the total cost of a typical nation-d variety.

As before, we solve for the endogenous nopoo1-

using the market-clearing condition. In this case,

the value that nation-o must sell is the full value of its M-sector output (not just its value added).

Under monopolistic competition‟s free entry assumption, the value of sales equals the value of

full costs, so the market clearing equation becomes:

],,[;111

ooooddoddooooo xPwCCEPpnCn

(8)

where the cost function C is given in (5). Solving (8) and plugging the result into (7) yields a

gravity equation modified to allow for intermediates goods trade, namely:

od

odododP

CEV

111

1

(9)

where Ed is defined in (7) and Co is defined in (8), and d ddodo EP11 .

Expression (9) is the gravity equation modified to allow for trade intermediates. The key

differences show up in the definition of the economic “mass” variables since purchases

are now driven both by consumer demand (for which income is the demand shifter) and

intermediate demand (for which total production costs is the demand shifter).

3. BREAKDOWN OF THE STANDARD GRAVITY MODEL

This theory exercise suggests a key difference that should arise between gravity estimates on

nations and time periods where most imports are consumer goods versus those where

intermediates trade is important. Specifically, the standard practice of using the GDP of origin

and destination countries as the „mass‟ variables in the gravity equations is inappropriate for

bilateral flows where parts and components are important. Of course, if the consumer- and

producer-demand moves in synch – as they may in a steady-state situation – then GDP may be a

reasonable proxy for both consumer and producer demand shifter. But if the role of vertical

specialisation trade is changing over time, GDP should be less good at proxy-ing for the

underlying demand shifters. For this reason, we expect that origin-country‟s GDP and destination

country‟s GDP will have diminished explanatory power for those countries where value-chain

trade is important.

These observations generate a number of testable hypotheses.

The estimated coefficient on the GDPs should be lower for nations where parts trade is important, and should fall as the importance of parts trade rises.

As vertical specialisation trade has become more important over time, the GDP point estimates should be lower for more recent years.

8

In those cases where the GDPs of the trade partners lose explanatory power, bilateral trade should be increasingly well explained by demand in third countries.

For example, China‟s imports should shift from being explained by China‟s GDP to being

explained by its exports to, say, the US and the EU. There are two ways of phrasing this

hypothesis. First, China‟s imports are a function of its exports rather than its own GDP. Second,

China‟s imports are a function of US and EU GDP rather than its own, since US and EU GDP

are critical determinants of their imports from China.

To check these conjectures, we estimate the standard gravity model for different sets of countries

and sectors for a panel that spans the years 1967 to 2007. We run standard log-linear gravity

equations using pooled cross-section time series data, namely:

odtodtdt

dt

ot

otodt

P

EYGV

lnln)ln( 211 (10)

A key econometric problem is that the price index Pdt and the market potential index ot are

unobservable and yet include factors that enter the regressions independently (e.g. E, Y and ).

Thus ignoring them can lead to serious biases.

If the econometrician is only interested in estimating the impact of a pair-specific variable – such

as distance or tariffs – the standard solution is to put in time-varying country-specific fixed

effects. This eliminates all the terms multiplied by 1 in equation (10). Plainly we cannot use this

approach to investigate the impact of using GDPs as the economic mass proxies when trade in

parts and components is important. We thus need other means of controlling for to

and dtP .

Our baseline specification accounts for the terms to

and dtP explicitly. As precise measures of

to and dtP

are hard to construct, we perform robustness checks using fixed effects

specifications. To ensure comparability with the fixed effects specification, in the key

specifications we enter the importer‟s and exporter‟s economic mass as a single product-term

into the equation, with the shortcoming of forcing the coefficient of the importer and exporter

mass variables to be the same. Specifically, the term accounting for the product of the trade

partners‟ economic mass is the product of importer-d real GDP (so to account for dtP ) and of

exporter-o‟s nominal GDP divided by a proxied for to

, constructed adapting a method first

introduced by Baier and Bergstrand (2001) namely:

11

1)(*d oddtot

DistGDP

The elasticity value in the to

relationship has been set as σ = 4, which corresponds to estimates

proposed in empirical literature (e.g. Obstfeld and Rogoff, 2001 and Carrere 2006).

Turning to the trade cost variable, , we introduce standard trade frictions, including log of

bilateral distance, and dummies for contiguity, and common language. Moreover for robustness

purposes we also test for additional time-varying trade frictions measured by cif-fob ratios, as

proposed by Bergstrand and Egger (2010).

The data used for the bilateral trade flows, and the cif-fob ratios are taken from the UN

COMTRADE database. GDPs are from the World Bank‟s World Development Indicators.

9

Bilateral distances, contiguity, and common language are from the CEPII database. Data for

Taiwan, which are missing from the UN databases, are from CHELEM (CEPII) and national

accounts.

Estimation is by simple ordinary least squares with the standard errors clustered by bilateral pairs

since we work in direction-specific trade flows rather than the more traditional average of

bilateral flows.

3.1. Empirical results

In Table 1 we report the gravity equation estimates for all goods as well as for intermediate and

final goods separately. Intermediate and final goods have been identified according to the UN

Broad Economic Categories Classification (see appendix). The sample includes all the nations

where data is available, namely 187 nations.

Coefficients have the expected signs and are statistically significant. For all six regressions (all

goods, only intermediates, and only consumer goods with and without time fixed effects) the

estimates are broadly similar. The mass variables are all estimated to be close to unity. The

bilateral distance variable is negative and falls in the expected range. The additional trade cost

measure, the cif/fob ratio, is always negative as expected for the sub-samples, but positive for the

aggregate sample. Continuity and language always have the expected sign and fall in the usual

ranges.

Table 1: Bilateral flows of total, intermediate and final goods, 187 nations, 2000-2007.

All goods Intermediates only Consumer goods only

VARIABLES (1) (2) (3) (4) (5) (6)

ln (GDPot*GDPdt/Ωot*Pdt) 0.860*** 0.865*** 0.898*** 0.905*** 0.791*** 0.796***

(0.006) (0.006) (0.007) (0.007) (0.008) (0.008)

ln(cif/fob ratio) -

0.0833*** -

0.0798*** -0.189*** -0.184*** -0.341*** -0.338***

(0.013) (0.013) (0.015) (0.015) (0.017) (0.017)

ln Distance -0.775*** -0.777*** -0.851*** -0.855*** -0.758*** -0.760***

(0.019) (0.019) (0.022) (0.022) (0.025) (0.025)

Contiguity 1.575*** 1.565*** 1.711*** 1.697*** 1.356*** 1.347***

(0.105) (0.105) (0.119) (0.119) (0.127) (0.127)

Common language 0.966*** 0.972*** 0.997*** 1.005*** 1.186*** 1.192***

(0.046) (0.046) (0.052) (0.052) (0.059) (0.059)

Constant -28.61*** -28.74*** -30.84*** -31.03*** -26.87*** -27.02***

(0.359) (0.363) (0.400) (0.404) (0.456) (0.459)

Time dummies

yes

yes

yes

Observations 62875 62875 62875 62875 58468 58468

R-squared 0.627 0.628 0.585 0.587 0.479 0.480

Source: Authors‟ calculations; Note: Dependent variable: imports + re-imports. Standard errors are clustered by bilateral pair. Robust

standard errors are reported in parenthesis: *** p

10

These Table 1 results confirm the findings of Bergstrand and Egger (2010), namely that the size

of the estimated coefficients does not vary for consumer and intermediate goods. As such, it

would seem that our concern about mis-estimating the gravity equation is misplaced. However,

as noted above, if the consumer and intermediate trade is roughly proportional over time, GDP

will be a reasonable proxy for both consumer income and gross value added. The real test of the

stability of the parameters would be on a sample where the importance of intermediates trade

was rising significantly.

Table 2: Bilateral flows of total goods among Factory Asia nations (1967-2008).

No time interactions Variable mass coefficient

VARIABLES (1) (2) (3) (4) (5) ln (GDPoGDPd/ΩoPd) 0.725*** 0.725*** 0.764*** 0.425*** 0.504***

(0.009) (0.028) (0.026) (0.055) (0.051)

*years 1967-1986

0.318*** 0.278***

(0.048) (0.048)

*years 1987-1996

0.177*** 0.164***

(0.027) (0.032)

*years 1998-2002

0.007 0.00274

(0.015) (0.017)

ln (Distance) -0.258*** -0.258

-0.0414

(0.0570) (0.298)

(0.297)

Contiguity 0.188*** 0.188

0.167

(0.0682) (0.386)

(0.367)

Colony -0.487*** -0.487

0.0695

(0.101) (0.388)

(0.405)

Common coloniser -0.620*** -0.620*

-0.296

(0.116) (0.325)

(0.324)

Constant -7.218*** -7.218*** -8.825*** -1.465 -2.632**

(0.433) (2.281) (0.485) (2.279) (1.178)

Time effects yes yes

Exporter*time effects

yes yes yes

Importer*time effects

yes yes yes Pair effects

yes yes yes

Clustered Standard Errors yes yes yes yes Observations 1722 1722 1722 1722 1722 R-squared 0.833 0.833 0.936 0.851 0.948

Source: Authors‟ calculations; Note: Standard errors are clustered by bilateral pair. Robust standard errors in parenthesis: *** p

11

coefficients which are 0.3 for the pre-Factory Asia period (Baldwin 2006), 0.2 for the 1987-1996

period, and essentially zero (and insignificant) for the post 1998 period.

Figure 1: GDP coefficients for Factory Asia countries, 1967-2008.

19851995

0

0.2

0.4

0.6

0.8

1

1.2

1967

1968

1969

1970

19

71

1972

1973

1974

1975

1976

19

77

1978

1979

1980

1981

1982

19

83

1984

1985

1986

1987

1988

19

89

1990

1991

1992

1993

1994

19

95

1996

1997

1998

1999

2000

20

01

2002

2003

2004

2005

2006

20

07

Year Coeficient

Note

s: Estimated mass-elasticity coefficients with year interactions and pair fixed effects (as in (10). High and low bars show plus/minus 2

standard errors; Factory Asia countries: Japan, Indonesia, Republic of Korea, Malaysia, Thailand, and Taiwan.

To estimate the mass variable‟s instability over time more clearly, we re-do the same regression

but allowing yearly interaction terms. The results, displayed in Figure 1, shows the evolution of

the GDP coefficients. The mass elasticity fall over time, with two clear breaks in the estimated

coefficients, 1985 and 1998.

The timing and direction of these structural changes are very much in line with the literature on

the internationalisation of production. According to many studies, production unbundling started

in the mid-1980s and accelerated in the 1990s (e.g. Hummels, Rapport and Yi 1998). The idea is

that coordination costs fell with the ICT revolution and this permitted the spatial bundling of

production stages (Baldwin 2006). The ICT revolution came in two phases. The internet came

online in a massive way in the mid-1980s, and then, in the 1990s, the price of

telecommunications plummeted with various ITC-related technical innovations and widespread

deregulation (Baldwin 2011). The upshot of all these changes was that it became increasingly

economical to geographically separate manufacturing stages. Stages of production that

previously were performed within walking distance to facilitate face-to-face coordination could

be dispersed without an enormous drop in efficiency or timeliness.

As far as the Figure 1 results are concerned, the notion is that as trade became increasingly

focused on intermediates, GDP became an increasingly poor determinant of trade flows – as

12

suggested by our theory. The impact of the mid-1980s changes and the mid-1990s changes are

clear from the estimated GDP elasticities. More specifically, from 1967 to 1985 the elasticity of

these countries‟ bilateral imports to GDP was stable, with a coefficient of about 0.77. Between

1985 and 1997, it steadily decreased to reach a coefficient value of about 0.60, and after 1998, it

further dropped to a figure close to 0.40. The coefficient estimates for the different periods in

Factory Asia are summarised in Table 2 , columns (4) and (5).

Table 3: Estimates for EU15, and US, Canada, Australia and New Zealand, 1967-2008.

VARIABLES No time interactions Variable mass coefficient

(1) (2) (3) (4) (5)

ln(GDPoGDPd/ΩoPd) 0.659*** 0.659*** 0.632*** 0.725*** 0.703***

(0.009) (0.025) (0.027) (0.058) (0.034)

*years 1967-1986

-0.0408 -0.0503

(0.051) (0.044)

*years 1987-1996

-0.0376 -0.0444

(0.036) (0.032)

*years 1998-2002

0.0132 0.005

(0.017) (0.014)

ln (Distance) -0.843*** -0.843***

-0.688**

(0.059) (0.233)

(0.276)

Constant -1.630** -1.630 -8.819*** -4.966 -10.72***

(0.726) (2.284) (0.657) (3.733) (0.917)

Time effects yes yes

Exporter*time effects

yes yes yes

Importer*time effects

yes yes yes

Pair effects

yes yes yes

Observations 820 820 820 820 820

R-squared 0.932 0.932 0.978 0.934 0.978

Clustered Standard Errors yes yes yes yes

Source: Authors‟ calculations; Note: Standard errors are clustered by bilateral pair. Robust standard errors are reported in parenthesis:

*** p

13

3.2. More precise estimates of the impact of components on the mass estimate

These two sets of results are highly suggestive. On data that is widely recognised as being

dominated by parts and components trade, we find structural instability in the mass variable

coefficient moving in the expected direction. However, on data where this sort of production

fragmentation is not widely viewed as having been important, we find that that mass point-

estimates are stable over time.

To explore this more systematically, we consider a more continuous relationship between the

importance of components trade and the point-estimate on the mass variable on the full sample.

Our basic assertion is that the composition of trade flows will influence the point estimates of the

economic mass variables since the standard gravity model is mis-specified when it comes to the

mass variable. The most direct test of this hypothesis is to include the ratio of intermediates to

total trade as a regressor, both on its own and – more importantly – as an interaction term with

the economic mass variable. Of course a mis-specification of one part of the regression has

implications for the point-estimates of the other regressors, so we also consider the ratio‟s

interaction with the other main regressors.

To this end, we re-estimate the basic equation on the full sample of 187 countries for the years

2000-2008 allowing for interactions with a variable that accounts for the share of intermediate

goods over total imports in each particular bilateral trade flow.

The idea here is that GDP as a measure for economic mass should work less well for those

bilateral flows that are marked by relatively high shares of intermediates trade. By estimating the

effect on the full sample, we avoid the problem of identifying the exact sources of the variation

in the coefficients. We implement the idea in two ways.

First we estimate the standard regression but include the share of bilateral imports that is in

intermediates (denoted as Mdinterm

/Md). This new variable is included on its own and interacted

with the other right-hand side variables. Table 4 reports the estimated results for the coefficients

of interest.

The regression results tend to confirm our hypothesis. The regression reported in column (1)

includes the ratio on its own and interacted only with the mass variable. The coefficients for

economic mass and distance are a very reasonable at 1.031 and -1.173 respectively (both

significant at the 1% level). The ratio on its own comes in positive as expected (bilateral trade-

links marked by a high share of intermediates tend to have „too much‟ trade compared to the

prediction of the standard gravity equation). The ratio interacted with economic mass also has a

negative sign, -0.129, which conforms with our hypothesis (the higher is the ratio of

intermediates for the particular trade pair, the lower is the estimate of the economic mass

variable). All coefficients are significantly different to zero at the 1% level of confidence.

The other columns report robustness checks on the main regression. The qualitative results on

the variables of interest (the mass coefficient, the ratio coefficient, and the mass*ratio interaction

coefficient) are robust to inclusion of interaction terms with any or all of the control variables.

This confirms the more informal tests based on an a priori separation of the sample.

Interestingly, the interaction term is also highly significant and negative for distance in

specification (2). That is, distance seems to matter more for components trade – a result that is

not in line with our simple model, but is expected from the broader literature on offshoring. For

14

example, transportation costs become more important when trade costs are incurred between

each stage of production while the value added per stage is modest.

Table 4: Interactions with share of intermediates in total imports, full sample.

VARIABLES (1) (2) (3) (4)

Mdinterm

/Md 6.536*** 8.018*** 6.954*** 7.330***

(0.858) (1.015) (0.835) (1.004)

ln (GDPoGDPd/ΩoPd) 1.031*** 1.027*** 1.064*** 1.058***

(0.010) (0.010) (0.010) (0.010)

* Mdinterm

/Md -0.129*** -0.118*** -0.137*** -0.126***

(0.017) (0.017) (0.017) (0.016)

ln (Distance) -1.173*** -1.051*** -1.011*** -0.954***

(0.018) (0.037) (0.0191 (0.037)

* Mdinterm

/Md

-0.232***

-0.110*

(0.059)

(0.0601

Contigod

1.350*** 0.967***

(0.101) (0.246)

* Mdinterm

/Md

0.625*

(0.369)

Common language

1.215*** 1.126***

(0.044) (0.078)

* Mdinterm

/Md

0.178

(0.119)

Constant -27.58*** -28.40*** -30.85*** -31.07***

(0.551) (0.634) (0.541) (0.625)

Observations 121737 121737 121737 121737

R-squared 0.604 0.604 0.621 0.621

Notes: Mdtinterm

/Md is the share of intermediate imports by a country d over its total imports. Robust standard errors are reported in

parenthesis: *** p

15

the 1% level. The additional effects lower the base case point-estimate by around 0.10. The

distance term is a very reasonable -1.1 and highly significant.

Table 5: All countries, 2000-2007, by share of intermediate imports.

Variables (GDPoGDPd/ΩoPd) ln(Distance) Constant

Base effect 0.985*** -1.105*** -26.29***

(0.018) (0.018) (0.898)

Base effect * d2 -0.0308

(0.021)

Base effect * d3 0.0108

(0.021)


(0.020)

Base effect * d5 -0.0803***

(0.020)


(0.021)


(0.021)


(0.022)


(0.024)

Base effect * d10 -0.0748*** (0.022)

Observations 121712 R-squared 0.610

Source: Authors‟ estimations; Note: deciles categorise countries bilateral imports by increasing shares of intermediate imports over total

imports. Hence q10 indicates the 10% bilateral import relationships where the share of intermediate imports in total imports is highest

and the base effect the 10% bilateral import relationships where the share of intermediate imports in total imports is lowest. Common

language and contiguity included by not reported. Standard errors are clustered by bilateral pair. Robust standard errors are reported in

parenthesis: *** p

16

0.8

0.9

0.9

1.0

1.0

1.1

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

siz

e c

oe

ffic

ien

t

share of intermediates in total imports

Source: Authors‟ estimations; Note: horizontal bars represent estimated coefficient and vertical bars twice the standard errors.

4. A SEARCH FOR MASS PROXIES WHEN INTERMEDIATES ARE IMPORTANT

The previous section provides clear evidence that the standard gravity equation is “broken” when

it comes to bilateral flows where intermediates trade is important. The theory suggests that the

perfect solution would require data on total costs to construct the demand shifter for

intermediates imports. If the economy is reasonably competitive, gross sales would be a good

proxy for the total costs. Unfortunately, such data are not available for a wide range of nations

especially the developing nations where production fragmentation is so important. On the mass

variable for the origin nation, theory suggests that we use gross output rather than value added.

Again such data are not widely available.

This section presents the results of our search for a pragmatic “repair” which relies only on data

that is available for a wide range of nations. The basic thrust is to use the theory in Section 2 to

develop some proxies for economic mass variables that better reflect the fact that the demand for

intermediates depends upon gross output, not value added.

4.1. Fixes for economic mass proxies

We start with the destination nation‟s mass variable. In Section 2 we showed that a bilateral flow

of total goods is the sum of goods whose demand depends upon the importing nation‟s GDP (i.e.

consumer goods) and goods whose demand depends upon the total costs of the sector buying the

relevant intermediates. The theory says that our economic mass measure should be a linear

combination of two mass measures, not a log-linear combination (see expressions (9) and (7)).

This suggests a first measure that adds imports of intermediates to GDP. The idea here is to

exploit the direct definition of total costs as the cost of primary inputs plus the value of

intermediate inputs. For any given local firm, some of the intermediates it purchases will be from

local suppliers, but summing across all sectors and firms within a single nation, such

intermediates will cancel out leaving only payments to local factors of production and imports of

17

intermediates. Our first pragmatic fix therefore is to measure the destination nation‟s demand

shifter by:

ointerm

iddd VYEi

, (11)

where Vinterm

is the value of bilateral imports of intermediates. If we summed across all partners,

this measure would include part of the bilateral flow to be explained (namely intermediates from

nation-o to nation-d). To avoid putting the trade flow to be explained on both sides of the

equation, we build the measure for each pair in a way that excludes the pair‟s bilateral trade.

For the economic mass variable size pertinent to the origin nation, we are trying to capture gross

output that must be sold. The proposed measure is a straightforward application of the theory; it

uses the origin nation‟s value added in manufacturing and its purchases of intermediate inputs

from all sources except from itself (due to a lack of data).

0i

,i

nterm

oi

manuf

oo VAVC (12)

Note that our specification of the gravity equation uses the exports from nation-o to nation-d, so

the second term in this does not include the bilateral flow to be explained. The second term

involves nation-o‟s imports from all nations, not its exports to nations.

4.2. Empirical results

To test whether these proposed proxies work better than GDP, we run regressions like those

reported in Table 4 but with the new proxies for economic mass replacing the standard proxy

(i.e. GDP). The results are shown in Table 6.

The results in Table 6 – compared with those in Table 4 – suggest that our proxies work better

than GDP. The key piece of evidence can be seen in column (1). This includes the ratio of

intermediates in total bilateral trade both on its own and interacted with the mass variable. The

lack of significant of the ratio in either role suggests that our new proxy is doing a better job than

GDP did in picking up demand and supply of intermediates.

Interestingly, the column (2) regression, which allows an interaction between distances on the

ratio of intermediates, suggests that the distance coefficient may also be mis-specified. When the

ratio is interacted with distance, the distance estimate falls somewhat on average but especially

for trade flows where parts and components are especially important (i.e. the ratio is high).

This suggests that distance is more important, not less, for bilateral trade flows dominated by

intermediates. The finding may reflect the well-known fact that most production fragmentation

arrangements are regional, not global (components trade is more regionalised that overall trade).

This result, however intriguing, does not really stand up to minor changes in the specification. In

regression (4), which includes the ratio‟s interaction with all variables, the distance result fades;

indeed only the common language effect seems to be magnified for trade flows marked by

particularly high ratios of intermediates.

Table 6: New mass proxies with share of intermediate, all nations, 2000-2007.

VARIABLES (1) (2) (3) (4)

18

Mdinterm

/Md 1.180 2.644** 2.044** 1.907*

(1.020) (1.142) (0.988) (1.143)

Ln (EdCo/ΩoPd) 0.898*** 0.889*** 0.945*** 0.932***

(0.012) (0.0116) (0.012) (0.012)

* Mdinterm

/Md -0.0322 -0.0132 -0.0289 -0.0247

(0.020) (0.020) (0.020) (0.020)

ln (Distance) -1.080*** -0.929*** -0.908*** -0.838***

(0.018) (0.038) (0.019) (0.038)

* Mdinterm

/Md

-0.279***

-0.131*

(0.065)

(0.067)

Contigod

1.441*** 1.211***

(0.092) (0.224)

*Mdinterm

/Md

0.356

(0.354)

Common language

1.251*** 1.047***

(0.047) (0.088)

* Mdinterm

/Md

0.385***

(0.143)

Constant -20.05*** -20.87*** -24.17*** -24.08***

(0.623) (0.687) (0.610) (0.685)

Observations 87258 87258 87258 87258

R-squared 0.607 0.607 0.631 0.631

Note: Robust standard errors are reported in parenthesis: *** p

19

Table 7: New mass proxies with intermediate deciles, all nations, 2000-2007.

Ln (EdCo/ΩoPd) ln (Distance) Constant

Base effect 0.877*** -1.051*** -19.29***

(0.022) (0.018) (1.074)


(0.024)

Base effect * d3 0.0365***

(0.025)


(0.024)


(0.024)

Base effect * d6 -0.0531**

(0.025)


(0.025)


(0.026)

Base effect * d9 -0.0652**

(0.028)

Base effect * d10 0.0102 (0.027)

Observations 87251 R-squared 0.609

Notes: See notes to Table 5.

5. WHY DO INCORRECTLY SPECIFIED MASS VARIABLES MATTER?

A large number of gravity studies focus on variable that vary across country pairs – say free

trade agreements, cultural ties, or immigrant networks. The most recent of these studies employ

estimators that control for the mass variables with fixed effects.8 Such studies do not suffer from

mass-variable mis-specification and so are unaffected by our critique.

There are however as mentioned in the introduction, a number of recent studies – especially

concerning the „distance puzzle‟ that do proxy for the production and demand variables with

GDP. It is these studies that our work speaks to.9

8 These econometric techniques were introduced by Harrigan (1996), Head and Mayer (2000),

and Combes, Lafourcade and Mayer (2005), Anderson and Van Wincoop (2003), and Feenstra

(2004).

9 Rauch (1999), Brun et al (2005), Berthelon and Freund (2008), Jacks et al (2008), and

Anderson and Van Wincoop (2003).

20

However, since most of these studies are concerned with a broad set of nations and commodities,

the mis-specification of the mass variable probably has a minor impact on the results – as the

findings of Bergstrand and Egger (2010) showed and we confirmed with our Table 1 results.

More worrying, however, is the use by authors that focus on trade in parts and components.10

These papers use the consumer-good version of the gravity model and thus mis-specify the mass

variable.

Once the equation is mis-specified – in particular the standard economic mass proxies are not

correctly reflecting the supply and demand constraints – we are in the realm of omitted variable

biases. The first task is to explore the nature of the biases that would arise from this mis-

specification. To simplify, assume away GDPs and distance and focus on a pair-wise policy

variable, say, nation-d‟s tariffs on imports from nation-o; we denote this as Tod. The estimated

gravity equation will have the following structure:

odtodtodt TV lnaconstantln 5 (13)

where the error is assumed to be iid.

Because intermediates supply is measured by total costs rather than GDP, and the supply of

intermediates that must be sold depends upon gross output rather than value added. This means

that the true model includes an additional term. That is:

odtodtodtodt ZTV lnalnaaln 650 (14)

where Zodt is the difference between the GDP-based mass variables and the true mass variables

as specified in (7). We can write Zodt as a function of Todt in an auxiliary regression:

odtodtodt uTbZ lnbln 10

(15)

where u is assumed to be iid. Using this notation for the coefficients of the auxiliary regression,

we can see that in estimating (13), we are actually estimating:

)(ln)aa()a(ln 616560 odtodtodtoodt uaTbabV

(16)

What this tells us is that the coefficient on the policy variable of interest will almost surely be

biased. The point is that the only way it is not biased is if there is no correlation between the mis-

specification of the economic mass variables and the policy variable.

What sort of correlation should we expect? Recall that the mis-measurement of the economic

mass variable all goes back to the importance of trade in intermediate goods. Since almost all

bilateral variables of interest are things that affect bilateral trade flows, it seems extremely likely

that the variable of interest will also affect the flow of intermediates. As long as it does, then we

know that the mis-specification of the mass variable will also lead to a bias in the pair-wise

variables.11

10 Athukorala and Yamashita (2006), Kimura et al (2007), Yokota and Kazuhiko (2008), and

Ando and Kimura (2009).

11 As noted above, the modern techniques for controlling for mass with time-varying country-

specific dummies eliminates such biases since they correctly control for the role of intermediates.

21

For example, let us suppose that tariffs discourage trade overall, but they especially discourage

intermediates trade (for the usual effective rate of protection reasons, i.e. the tariff is paid on the

gross trade value but its incidence falls on the value added only). In this case, we should expect

low tariffs to encourage two things, an overall increase in trade and an increase in the ratio of

intermediates. In this case, the bias in the mis-specified gravity equation is likely to be negative,

since the policy variable is negatively correlated with the omitted variable. Furthermore, the mis-

specification also affects the standard errors, which would result in a biased inference

(Wooldridge, 2003, ch.4).

6. CONCLUDING REMARKS

In this paper we present empirical evidence that the standard gravity model performs poorly by

some measures when it is applied to bilateral flows where parts and components trade is

important. The paper also provides a simple theoretical foundation for a modified gravity

equation that is suited to explaining trade where international supply chains are important.

Finally we suggest ways in which the theoretical model can be implemented empirically.

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APPENDIX

Classification for intermediate and final goods

BEC categories

Intermediate goods: 111 - Primary food and beverages, mainly for industry

121 - Processed food and beverages, mainly for industry

21 - Primary industrial supplies not elsewhere specified

22 - Processed industrial supplies not elsewhere specified

32 - Processed fuels and lubricants

42 - Parts and accessories of capital goods (except transport

equipment)

53 - Parts and accessories of transport equipment

Consumption goods: 112 - Primary food and beverages, mainly for household consumption

122 – Processed food and beverages, mainly for industry

51 - Passenger motor cars

6 - Consumer goods not elsewhere specified

Other: 31 - Primary fuels and lubricants

41 - Capital goods, excluding parts and components

51 - Other transport equipment

7 - Other

Source: Comtrade‟s Broad Economic Categories; for details see

http://unstats.un.org/unsd/tradekb/Knowledgebase/Intermediate-Goods-in-Trade-Statistics
http://unstats.un.org/unsd/tradekb/Knowledgebase/Intermediate-Goods-in-Trade-Statistics

gravity chains: estimating bilateral trade flows when parts ......for example, rauch (1999), brun et...

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